Octagon Formula

A polygon is a two-dimensional (2-D) closed figure made up of straight line segments. In geometry, the octagon is a polygon with 8 sides. If the lengths of all the sides and the measurement of all the angles are equal, the octagon is called a regular octagon. In other words, the sides of a regular octagon are congruent. Each of the interior angle and the exterior angle measure 135° and 45° respectively, in a regular octagon. There is a predefined set of formulas for the calculation of perimeter, and area of a regular octagon which is collectively called as octagon formula. For an octagon with the length of its edge as “a”, the formulas are listed below.

Octagon Formulas

Formulas for Octagon

Area of an Octagon

2a2(1+√2)

Perimeter of an Octagon

8a

Octagon formula helps us to compute the area and perimeter of octagonal objects.

Derivation of Octagon Formulas:

Consider a regular octagon with each side “a” units.

Formula for Area of an Octagon:

Area of an octagon is defined as the region occupied inside the boundary of an octagon.

In order to calculate the area of an octagon, we divide it into small eight isosceles triangles. Calculate the area of one of the triangles and then we can multiply by 8 to find the total area of the polygon.

Take one of the triangles and draw a line from the apex to the midpoint of the base to form a right angle. The base of the triangle is a, the side length of the polygon and OD is the height of the triangle.